CN102968553B - A kind of aircraft lands risk evaluation method - Google Patents

Abstract

The present invention relates to a kind of risk evaluation method, particularly to a kind of aircraft lands process risk evaluating method based on fuzzy multi-attribute group decision.The present invention comprises the steps: that (1) sets up landing mission multistage risk evaluation and test matrix；(2) efficiency evaluation index is set up；(3) different landing period attribute weight is formulated；(4) evaluation and test landing risk.The present invention is directed to the complexity of aircraft lands process entirety evaluation and test, four Main Stage state of flight information in right combination landing mission, the vague description of LUFENG danger is faced toward according to expert, design fuzzy multi-attribute group decision algorithm, realize the sequence comparison of multi-aircraft landing mission flight risk, overcome traditional decision method quantity of information little, decision mode is single, the result of decision lacks integrity, the shortcomings such as overall landing mission can not be evaluated and tested, comprehensive multistage decision information, decision making approach is advanced, more system provides the integrated risk of aircraft lands process to evaluate and test effectively.

Description

A kind of aircraft lands risk evaluation method

Technical field

The present invention relates to a kind of risk evaluation method, particularly to a kind of flight based on fuzzy multi-attribute group decision Device landing mission risk evaluation method.

Background technology

Aircraft lands process condition is complicated and changeable, is the multiple stage of accident.Aircraft from normal flat fly status transition to Land halted state is divided into decline stage, flare phase, ground connection stage and the stage of alightinging run, and driver is driven by manipulation Bar change of flight device state of flight so that it is safe falling is to land.Due in landing mission, aircraft self six degree of freedom position Put, the quantity of state such as speed, acceleration and flight attitude changes greatly, if pilot control is improper or landing bad environments, and will Bigger landing risk can be produced.

Main in terms of final landing effect and landing data index two for the evaluation and test of aircraft lands process risk at present Analyze: final landing effect be judge can safe falling on ground, if there is the loss of body and personnel, this is one Rigid index, if there is accident, this time lands and assert unsuccessfully, greatest risk；And landing data index mainly includes ground connection Speed, distance of landing run and landing distance, this is the major part for the evaluation and test of aircraft lands process risk.Touchdown speed Represent that aircraft main wheel comes into contact with the horizontal velocity of ground moment, distance of landing run represent from main-gear touchdown point start sliding run to Aircraft stop the horizontal range of process, landing distance represent aircraft from safe altitude start to sliding run stop the level of process Distance.

Tradition risk evaluation method is in the case of clear and definite final landing effect safety, for a certain aircraft type, system The standard value of fixed above-mentioned each landing data index, compares this standard value with when the corresponding index value of On the Last Voyages landing mission Right, comparison deviation is the least, and this time landing risk is the least.This method only accounts for the ground connection stage and alightings run the performance in stage Index, have ignored the decline stage of landing mission and the potential risk of flare phase, lacks the analysis for overall landing mission； Tradition risk evaluation method only analyzes above three landing data index, the most comprehensively examines aircraft six degree of freedom quantity of state Considering, evaluation and test quantity of information is less；Tradition risk evaluation method has been compared wind by current performance index and established standards value Danger judges, decision method is single, and result lacks integrity；To sum up, traditional risk evaluation method can not realize aircraft lands The comprehensive overall evaluation and test of process.

Summary of the invention

It is an object of the invention to provide one more completely, more system, more effective aircraft lands process synthesis risk Evaluating method.

The object of the present invention is achieved like this:

A kind of aircraft lands usefulness evaluating method, comprises the steps:

(1) landing mission multistage risk evaluation and test matrix is set up: record the Flight Condition Data of all aircraft, including flying Line position g_x,g_y,g_z, flight speed v_x,v_y,v_zWith flight attitude α, β, wherein g_xFor aircraft Longitudinal Flight position, g_yFor flight Device horizontal flight position, g_zFor the vertical flight position of aircraft, v_xFor aircraft Longitudinal Flight speed, v_yLaterally fly for aircraft Line speed, v_zFor the vertical flight speed of aircraft, α is the aircraft flight angle of attack, and β is aircraft flight yaw angle, to declining In journey, the aircraft usefulness in decline stage, flare phase, ground connection stage and the stage of alightinging run is described, and sets up aircraft and Land process multistage risk evaluation and test matrix；

(2) efficiency evaluation index is set up: using landing mission four-stage as group decision person, aircraft flight state variable As decision object attribute, different phase expert describes as evaluation metrics for the language of aircraft lands risk, if X= {x₁,x₂,…x_mIt is that m aircraft is optionally gathered, wherein x_iFor i-th aircraft；U={u₁,u₂,…u_mIt is right The state of flight community set answered, wherein u_jFor jth state of flight attribute；D={d₁,d₂,d₃,d₄It is that four-stage is as certainly Plan person gathers, wherein d₁Represent decline stage, d₂Represent flare phase, d₃Represent ground connection stage, d₄Represent and alighting run the stage； For different phase d_k∈ D provides aircraft x_i∈ X is in state of flight u_jLanding risk under ∈ U describes r_ij ^(k), it is thus achieved that evaluation and test square Battle array R_k=(r_ij ^(k))_m×n；

(3) formulate different landing period attribute weight, determine that each stage relative priority weight matrix is:

ω^(k)={ ω₁ ^(k),ω₂ ^(k),ω₃ ^(k),...,ω_n ^(k)}^T, wherein ω_i ^(k)For in aircraft lands kth phase process The attribute weight of i-th quantity of state；

(4) evaluation and test landing risk:

1) according to the possibility degree computing formula of 3 σ rule definition normal fuzzy linguistic variables, fixed under Normal Fuzzy-number framework Justice n ties up normal fuzzy language weighted average operator；

2) utilize n dimension normal fuzzy language weighted average operator to evaluation and test matrix R_kIn the i-th row fuzzy language evaluation and test letter Breath is assembled, and obtains d_kStage aircraft x_iSynthesized attribute evaluation and test, synthesized attribute evaluation result r_i ^(k), i ∈ M, k=1,2, 3,4, assemble, obtain aircraft x_iThe evaluation and test of colony synthesized attribute；

3) to r_i(i ∈ M) compares two-by-two, sets up Possibility Degree Matrix P=(p_ij)_m×n, wherein p_ijRepresent r_iMore than r_j's Possibility degree；Obtain the ordering vector ω of P^P=(ω₁ ^P,ω₂ ^P,…ω_m ^P)^T, wherein ω_i ^PRepresent the relative order of i-th aircraft Vector magnitude, utilizes ω_i ^PTo colony synthesized attribute evaluation and test r_iIt is ranked up, aircraft lands risk is ranked up and preferentially.

The beneficial effects of the present invention is:

The present invention is directed to the complexity of aircraft lands process entirety evaluation and test, four main rank in right combination landing mission Section state of flight information, according to expert facing to the vague description of LUFENG danger, designs fuzzy multi-attribute group decision algorithm, it is achieved fly more The sequence comparison of row device landing mission flight risk, overcomes traditional decision method quantity of information little, and decision mode is single, and decision-making is tied Fruit lacks integrity, it is impossible to the shortcomings such as the overall landing mission of evaluation and test, comprehensive multistage decision information, decision making approach is advanced, is more System provides the integrated risk evaluation and test of aircraft lands process effectively.

Accompanying drawing explanation

Fig. 1 is that landing risk based on fuzzy multi-attribute group decision evaluates and tests flow chart；

Fig. 2 is Normal Fuzzy-number schematic diagram.

Detailed description of the invention

It is a kind of aircraft lands process wind based on fuzzy multi-attribute group decision described in present embodiment as shown in Figure 1 Danger evaluating method, it is as follows that it is embodied as step:

1 sets up landing mission multistage risk evaluation and test matrix

During aircraft lands, measured and storage system record entirety Flight Condition Data by on-board data, fly Line position (g_x,g_y,g_z), flight speed (v_x,v_y,v_z) and the quantity of state such as flight attitude (α, β), wherein g_xLongitudinally fly for aircraft Line position, g_yFor aircraft horizontal flight position, g_zFor the vertical flight position of aircraft, v_xFor aircraft Longitudinal Flight speed, v_y For aircraft horizontal flight speed, v_zFor the vertical flight speed of aircraft, α is the aircraft flight angle of attack, and β is aircraft flight side Sliding angle, and data set is stored in computer.

Landing mission is divided into four-stage: decline stage, flare phase, ground connection stage and the stage of alightinging run.Foundation The Flight Condition Data collection set up, with reference to ideal flight flight path, speed and attitude for the aforementioned four stage, to aircraft lands Risk is described.Consider that actual flight state describes and be vulnerable to experience, knowledge and profile's impact, there is non-thread The features such as property, complexity and ambiguity, during actual analysis, the evaluation information of decision scheme should be Fuzzy Linguistic Variable.At mould Sticking with paste in the selection of membership function, Normal Fuzzy-number, closest to human thinking, is portrayed the most applicable, therefore uses normal fuzzy language As evaluation index.

Definition 1: setFor normal fuzzy linguistic variable, as in figure 2 it is shown, its membership functionR→ [0,1] it is expressed as follows:

${\mathrm{\μ}}_{{\hat{S}}_{\mathrm{\θ}}}\left(\mathrm{\τ}\right)=e^{-\left(\frac{\mathrm{\τ}-{\mathrm{\τ}}_{\mathrm{\θ}}}{{\mathrm{\σ}}_{\mathrm{\θ}}}\right)},\left({\mathrm{\σ}}_{\mathrm{\θ}}>0\right)---\left(1\right)$

Wherein:τ_θAnd σ_θRepresent expectation and the variance of normal fuzzy linguistic variable respectively.

Normal Fuzzy-number has the property that

IfWithIt is respectively two normal fuzzy linguistic variables, and λ ∈ [0,1], then has:

(1) $\mathrm{\λ}{\hat{s}}_1=\mathrm{\λ}\[{\mathrm{\τ}}_{{\mathrm{\θ}}_1},{\mathrm{\σ}}_{{\mathrm{\θ}}_1}\]=\[{\mathrm{\λ\τ}}_{{\mathrm{\θ}}_1},{\mathrm{\λ\σ}}_{{\mathrm{\θ}}_1}\]$

(2) ${\hat{s}}_1+{\hat{s}}_2=\[{\mathrm{\τ}}_{{\mathrm{\θ}}_1},{\mathrm{\σ}}_{{\mathrm{\θ}}_1}\]+\[{\mathrm{\τ}}_{{\mathrm{\θ}}_2},{\mathrm{\σ}}_{{\mathrm{\θ}}_2}\]=\[{\mathrm{\τ}}_{{\mathrm{\θ}}_1}+{\mathrm{\τ}}_{{\mathrm{\θ}}_2},{\mathrm{\σ}}_{{\mathrm{\θ}}_1}+{\mathrm{\σ}}_{{\mathrm{\θ}}_2}\]$

Repeat above-mentioned evaluation and test step, be evaluated for different aircraft lands states, set up for four-stage different Aircraft lands risk evaluation and test matrix.

2 set up Risk Evaluation Factors

During fuzzy multi-attribute group decision issue handling, need to select multiple policymaker, respectively decision scheme is carried out Evaluation and test, last comprehensive multiple results of decision carry out integral evaluation, and landing mission risk evaluation and test it is important that Appropriate application is each Land stage state of flight information carries out the comprehensive evaluating of landing overall process, if each landing period is generalized for policymaker, then Different phase expert describes for the landing risk of different aircraft can be as different policymaker for the evaluation and test of decision scheme Index, then landing risk evaluation and test just can be converted into multi-attribute group decision making problem and go to process, and wherein policymaker is four landing rank Section, decision scheme is the different phase expert description for aircraft lands risk, and scheme attribute is aircraft flight state, as Shown in table 1.

Table 1 lands risk expert's evaluation and test table

If X={x₁,x₂,...x_mIt is that m aircraft optionally collects, wherein x_iFor i-th aircraft；U={u₁, u₂,...u_nIt is corresponding state of flight community set, wherein u_jFor jth state of flight attribute；D={d₁,d₂,d₃,d₄Is Four landing periods collect as policymaker, wherein d₁Represent decline stage, d₂Represent flare phase, d₃Represent ground connection stage, d₄Table Show the stage of alightinging run；For different phase d_k∈ D provides aircraft x_i∈ X is in state of flight u_jNormal fuzzy risk under ∈ U DescribeObtain risk evaluation and test matrix

u₁ u₂ ...... u_n

$R_k=\left[\begin{array}{cccc}{r}_{11}^{\left(k\right)}& r_{12}^{\left(k\right)}& ...& r_{1n}^{\left(k\right)}\\ r_{21}^{\left(k\right)}& r_{22}^{\left(k\right)}& ...& r_{2n}^{\left(k\right)}\\ ...& ...& ...& ...\\ r_{m1}^{\left(k\right)}& r_{m2}^{\left(k\right)}& ...& r_{mn}^{\left(k\right)}\end{array}\right]\begin{array}{c}{x}_1\\ x_2\\ ...\\ x_m\end{array}---\left(2\right)$

Its risk describes list For normal fuzzy linguistic scale, the expression-form corresponding with this scale is:

s₁=[0.1,0.04], s₂=[0.2,0.04], s₃=[0.3,0.04],

s₄=[0.4,0.05], s₅=[0.5,0.05], s₆=[0.6,0.05],

s₇=[0.7,0.04], s₈=[0.8,0.04], s₉=[0.9,0.04].

3 determine relative priority weight

Determining evaluation and test matrix R_kAfter, the key of risky decision making just determines that single policymaker d_kProvide decision scheme x_iBelong to Property evaluation and test r_i ^(k)Attribute weight vector ω^(k)With decision scheme x_iColony synthesized attribute evaluation and test r_iAttribute weight vector ω.

For aircraft flight state relative priority weight, whereinFor kth stage mistake The attribute weight of i-th quantity of state in journey；Due to aircraft flight effect mainly by flight position (g_x,g_y,g_z), flight speed (v_x,v_y,v_z) and 8 main state variables such as flight attitude (α, β) weigh, it is considered to the differential relationship of Position And Velocity, each state Amount relative priority weight relationship is:

${\mathrm{\ω}}_{g_x}={\mathrm{\ω}}_{g_{{}_y}}={\mathrm{\ω}}_{g_z}>{\mathrm{\ω}}_{v_x}={\mathrm{\ω}}_{v_y}={\mathrm{\ω}}_{v_z}={\mathrm{\ω}}_{\mathrm{\α}}={\mathrm{\ω}}_{\mathrm{\β}}---\left(3\right)$

Concrete numerical value is determined by expert, but should ensure that when weight properties assignment:

ω={ ω₁,ω₂,...ω_t}^TFor different landing period relative priority weights, wherein ω_iIt it is the attribute in the i-th stage Weight；According to each stage for the material impact of landing risk, determine that landing period relative priority weight matrix is ω^(k)= {0.2,0.2,0.4,0.2}^T。

4 aircraft lands risk based on normal fuzzy multi-attribute group decision making evaluation and tests

1) the possibility degree computing formula of 3 σ rule definition normal fuzzy linguistic variables it is first depending on:

Definition 2: setDefinition normal fuzzy linguistic variable ${\hat{s}}_1\≥{\hat{s}}_2$ Possibility degree $p({\hat{s}}_1\≥{\hat{s}}_2)$ For:

$p({\hat{s}}_1\≥{\hat{s}}_2)=max\{1-max(\frac{{\hat{s}}_2^{+}-{\hat{s}}_1^{-}}{l_2+l_1},0),0\}---\left(4\right)$

$\left\{\begin{array}{c}{\hat{s}}_i^{+}={\mathrm{\τ}}_{{\mathrm{\θ}}_i}+2.58{\mathrm{\σ}}_{{\mathrm{\θ}}_i}\\ {\hat{s}}_i^{-}={\mathrm{\τ}}_{{\mathrm{\θ}}_i}-2.58{\mathrm{\σ}}_{{\mathrm{\θ}}_i}\\ l_i={\hat{s}}_i^{+}-{\hat{s}}_i^{-}\end{array}\right.,(i=1,2)$

Possibility degree p has a following Operation Nature:

(1) $0\≤p({\hat{s}}_1\≥{\hat{s}}_2)\≤1,0\≤p({\hat{s}}_2\≥{\hat{s}}_1)\≤1;$

(2) $p({\hat{s}}_1\≥{\hat{s}}_2)+p({\hat{s}}_2\≥{\hat{s}}_1)=1,$ Especially, when ${\hat{s}}_1={\hat{s}}_2$ Time, $p({\hat{s}}_1\≥{\hat{s}}_2)=p({\hat{s}}_2\≥{\hat{s}}_1)=1/2;$

(3) set $p({\hat{s}}_1\≥{\hat{s}}_2)\≥1/2$ And $p({\hat{s}}_2\≥{\hat{s}}_3)\≥1/2,$ Then $p({\hat{s}}_1\≥{\hat{s}}_3)\≥1/2;$

(4) set $p({\hat{s}}_1\≥{\hat{s}}_2)\≥1/2$ And $p({\hat{s}}_2\≥{\hat{s}}_3)\≥1/2,$ Then $p({\hat{s}}_1\≥{\hat{s}}_2)+p({\hat{s}}_2\≥{\hat{s}}_3)\≥p({\hat{s}}_1\≥{\hat{s}}_3)$

2) Normal Fuzzy-number framework give a definition n tie up normal fuzzy language weighted average (NFLWA) operator:

Definition 3: set f: ${\hat{s}}^n\→\hat{s},$ If $f\left({\hat{s}}_1,{\hat{s}}_2,\mathrm{...},{\hat{s}}_n\right)={\mathrm{\ω}}_1{\hat{s}}_1\⊕{\mathrm{\ω}}_2{\hat{s}}_2\⊕...\⊕{\mathrm{\ω}}_n{\hat{s}}_n,$ Wherein ω=(ω₁, ω₂,...ω_n)^TIt is the weighing vector being associated with f, ω_j∈ [0,1],Then claiming function f is that n ties up normal fuzzy Language weighted average (NFLWA) operator.

${\mathrm{NFLWA}}_{\mathrm{\ω}}\left({\hat{s}}_1,{\hat{s}}_2,\mathrm{...},{\hat{s}}_n\right)={\mathrm{\ω}}_1{\hat{s}}_1\⊕{\mathrm{\ω}}_2{\hat{s}}_2\⊕...\⊕{\mathrm{\ω}}_n{\hat{s}}_n=\[{\Σ}_{j=1}^n{\mathrm{\ω}}_j{x}_{{\mathrm{\θ}}_j},{\Σ}_{j=1}^n{\mathrm{\ω}}_j{\mathrm{\σ}}_{{\mathrm{\θ}}_j}\]---\left(5\right)$

3) realizing landing risk based on normal fuzzy linguistic variable multi-attribute group decision making evaluation and test, its steps in decision-making is as follows:

(1) for a certain multi-attribute group decision making problem, if X, U and D are respectively scheme (aircraft) collection, attribute (flight shape State) collect and policymaker's (landing period) collection.Policymaker d_k∈ D provides scheme x_i∈ X is at attribute u_jFuzzy language evaluation and test under ∈ UAnd obtain risk evaluation and test matrix

(2) utilize NFLWA operator that risk is evaluated and tested matrix R_kIn the i-th row fuzzy language evaluation and test information assemble, To d_kLanding period aircraft x_iSynthesized attribute is evaluated and tested:

$r_i^{\left(k\right)}={\mathrm{NFLWA}}_{{\mathrm{\ω}}^{\left(k\right)}}(r_{i1}^{\left(k\right)},...,r_{in}^{\left(k\right)})={\mathrm{\ω}}_1^{\left(k\right)}{r}_{i1}^{\left(k\right)}+...+{\mathrm{\ω}}_n^{\left(k\right)}{r}_{in}^{\left(k\right)},(i\∈M,k=1,2,3,4)---\left(6\right)$

(3) the aircraft x that four-stage is given by recycling NFLWA operator_iSynthesized attribute evaluation and test r_i ^(k)(i ∈ M, k= 1,2,3,4) assemble, obtain aircraft x_iThe evaluation and test of colony synthesized attribute:

r_i=NFLWA_ω(r_i ⁽¹⁾,...,r_i ⁽⁴⁾)=ω₁r_i ⁽¹⁾+...+ω₄r_i ⁽⁴⁾(i ∈ M) (7) r here_iFor positive morphotype Stick with paste virtual linguistic variable.

(4) to r_i(i ∈ M) compares two-by-two, remembers p_ij=p (r_i＞ r_j), set up Possibility Degree Matrix P=(p_ij)_m×m, its Middle p_ijRepresent r_iMore than r_jPossibility degree；；Understanding according to possibility degree algorithm, matrix P is Complementary Judgement Matrix, according to complementary Judgment matrix sort formula:

${\mathrm{\ω}}_i^p=\frac{1}{m(m-1)}(\underset{j=1}{\overset{m}{\Σ}}{p}_{ij}+\frac{m}{2}-1)---\left(8\right)$

Obtain the ordering vector of matrix PWherein ω_i ^PRepresent the relative order of i-th aircraft Vector magnitude.

(5) ω is utilized_i ^P(i ∈ M) is to colony synthesized attribute evaluation and test r_iIt is ranked up, and then to aircraft lands risk x_iEnter Row sorts and preferentially, finally realizes the evaluation and test of landing risk.

Claims (1)

1. an aircraft lands usefulness evaluating method, is characterized in that, comprises the steps:

(1) landing mission multistage risk evaluation and test matrix is set up: record the Flight Condition Data of all aircraft, including flight position Put g_x,g_y,g_z, flight speed v_x,v_y,v_zWith flight attitude α, β, wherein g_xFor aircraft Longitudinal Flight position, g_yHorizontal for aircraft To flight position, g_zFor the vertical flight position of aircraft, v_xFor aircraft Longitudinal Flight speed, v_yFor aircraft horizontal flight speed Degree, v_zFor the vertical flight speed of aircraft, α is the aircraft flight angle of attack, and β is aircraft flight yaw angle, during declining The aircraft usefulness in decline stage, flare phase, ground connection stage and the stage of alightinging run is described, and sets up aircraft lands mistake Journey multistage risk evaluation and test matrix；

(2) efficiency evaluation index is set up: using landing mission four-stage as group decision person, aircraft flight state variable conduct Decision object attribute, different phase expert describes as evaluation metrics for the language of aircraft lands risk, if X={x₁, x₂,…x_i…x_mIt is that m aircraft is optionally gathered, wherein x_iFor i-th aircraft；U={u₁,u₂,…u_j…u_n} For corresponding state of flight community set, wherein u_jFor jth state of flight attribute；D={d₁,d₂,d₃,d₄It is that four-stage is made Gather for policymaker, wherein d₁Represent decline stage, d₂Represent flare phase, d₃Represent ground connection stage, d₄Represent and alighting run rank Section；For different phase d_k∈ D provides aircraft x_i∈ X is in state of flight u_jLanding risk under ∈ U describes r_ij ^(k), for not With stage d_k∈ D provides aircraft x_i∈ X is in state of flight u_jNormal fuzzy risk under ∈ U describesObtain evaluation and test square Battle array R_k=(r_ij ^(k))_m×n；

Its risk describes list For normal fuzzy linguistic scale, the expression-form corresponding with this scale is:

s₁=[0.1,0.04], s₂=[0.2,0.04], s₃=[0.3,0.04],

s₄=[0.4,0.05], s₅=[0.5,0.05], s₆=[0.6,0.05],

s₇=[0.7,0.04], s₈=[0.8,0.04], s₉=[0.9,0.04]；

(3) formulate different landing period attribute weight, determine that each stage relative priority weight matrix is:

ω^(k)={ ω₁ ^(k),ω₂ ^(k),ω₃ ^(k),...ω_j ^(k)...,ω_n ^(k)}^T, wherein ω_j ^(k)For aircraft lands kth stage mistake The attribute weight of jth quantity of state in journey；

Aircraft flight effect is by flight position g_x,g_y,g_z, flight speed v_x,v_y,v_zCome with flight attitude α, β totally 8 quantity of states Weighing, each quantity of state relative priority weight relationship is:

${\mathrm{\ω}}_{g_x}={\mathrm{\ω}}_{g_y}={\mathrm{\ω}}_{g_z}>{\mathrm{\ω}}_{v_x}={\mathrm{\ω}}_{v_y}={\mathrm{\ω}}_{v_z}={\mathrm{\ω}}_{\mathrm{\α}}={\mathrm{\ω}}_{\mathrm{\β}}$

Ensure when weight properties assignment:

(4) evaluation and test landing risk:

1) according to the possibility degree computing formula of 3 σ rule definition normal fuzzy linguistic variables, give a definition n at Normal Fuzzy-number framework Dimension normal fuzzy language weighted average operator；

Possibility degree computing formula according to 3 σ rule definition normal fuzzy linguistic variables: WithWithRepresent normal fuzzy linguistic variable s respectively₁And s₂Expectation and variance, define normal fuzzy linguistic variablePossibility degreeFor:

$p({\hat{s}}_1\≥{\hat{s}}_2)=max\{1-max(\frac{{\hat{s}}_2^{+}-{\hat{s}}_1^{-}}{l_2+l_1},0),0\}$

$\left\{\begin{array}{c}{\hat{s}}_i^{+}={\mathrm{\τ}}_{{\mathrm{\θ}}_i}+2.58{\mathrm{\σ}}_{{\mathrm{\θ}}_i}\\ {\hat{s}}_i^{-}={\mathrm{\τ}}_{{\mathrm{\θ}}_i}-2.58{\mathrm{\σ}}_{{\mathrm{\θ}}_i}\\ l_i={\hat{s}}_i^{+}-{\hat{s}}_i^{-}\end{array}\right.,i=1,2$

Possibility degree p has a following Operation Nature:

$0\≤p({\hat{s}}_1\≥{\hat{s}}_2)\≤1,0\≤p({\hat{s}}_2\≥{\hat{s}}_1)\≤1;$

WhenTime,

IfAndThen

IfAndThen

2) utilize n dimension normal fuzzy language weighted average operator to evaluation and test matrix R_kIn the i-th row fuzzy language evaluation and test information assemble, Obtain d_kStage aircraft x_iSynthesized attribute evaluation and test, synthesized attribute evaluation result r_i ^(k), i ∈ m, k=1,2,3,4, assemble, obtain Aircraft x_iThe evaluation and test of colony synthesized attribute；IfIfWherein ω=(ω₁,ω₂,...ω_n)^TIt is the weighing vector being associated with f, ω_j∈ [0,1],Then claiming function f is n dimension Normal fuzzy language weighted average NFLWA operator；

${\mathrm{NFLWA}}_{\mathrm{\ω}}({\hat{s}}_1,{\hat{s}}_2,\mathrm{...}{\hat{s}}_n)={\mathrm{\ω}}_1{\hat{s}}_1\⊕{\mathrm{\ω}}_2{\hat{s}}_2\⊕\mathrm{...}\⊕{\mathrm{\ω}}_n{\hat{s}}_n=\[{\mathrm{\Σ}}_{j=1}^n{\mathrm{\ω}}_j{\mathrm{\τ}}_{{\mathrm{\θ}}_j},{\mathrm{\Σ}}_{j=1}^n{\mathrm{\ω}}_j{\mathrm{\σ}}_{{\mathrm{\θ}}_j}\];$

3) to r_iCompare two-by-two, i ∈ m, set up Possibility Degree Matrix P=(p_ij)_m×n, wherein p_ijRepresent r_iMore than r_jPossibility Degree；Obtain the ordering vector ω of P^P=(ω₁ ^P,ω₂ ^P,…ω_i ^P…ω_m ^P)^T, wherein ω_i ^PRepresent the relative row of i-th aircraft Sequence vector magnitude, utilizes ω_i ^PTo colony synthesized attribute evaluation and test r_iIt is ranked up, aircraft lands risk is ranked up and selects Excellent；

(3.1) for multi-attribute group decision making problem, if X, U and D are respectively scheme collection, property set and policymaker's collection；Policymaker d_k∈ D provides scheme x_i∈ X is at attribute u_jFuzzy language evaluation and test under ∈ UAnd obtain risk evaluation and test matrix

(3.2) utilize NFLWA operator that risk is evaluated and tested matrix R_kIn the i-th row fuzzy language evaluation and test information assemble, obtain d_k Landing period aircraft x_iSynthesized attribute is evaluated and tested:

$\begin{array}{cc}{r}_i^{\left(k\right)}={\mathrm{NFLWA}}_{{\mathrm{\ω}}^{\left(k\right)}}(r_{i1}^{\left(k\right)},\mathrm{...},r_{in}^{\left(k\right)})={\mathrm{\ω}}_1^{\left(k\right)}{r}_{i1}^{\left(k\right)}+\mathrm{...}+{\mathrm{\ω}}_n^{\left(k\right)}{r}_{in}^{\left(k\right)}& i\∈m,k=1,2,3,4\end{array};$

(3.3) the aircraft x that four-stage is given by recycling NFLWA operator_iSynthesized attribute evaluation and test r_i ^(k), i ∈ m, k=1, 2,3,4 assemble, and obtain aircraft x_iThe evaluation and test of colony synthesized attribute:

r_i=NFLWA_ω(r_i ⁽¹⁾,...,r_i ⁽⁴⁾)=ω₁r_i ⁽¹⁾+...+ω₄r_i ⁽⁴⁾, i ∈ m

Here r_iFor the virtual linguistic variable of normal fuzzy；

(3.4) to r_iCompare two-by-two, i ∈ m, remember p_ij=p, r_i＞ r_j, set up Possibility Degree Matrix P=(p_ij)_m×n, wherein p_ij Represent r_iMore than r_jPossibility degree；Understanding according to possibility degree algorithm, matrix P is Complementary Judgement Matrix, judges square according to complementary Battle array sort formula:

${\mathrm{\ω}}_i^P=\frac{1}{m(m-1)}(\underset{j=1}{\overset{m}{\Σ}}{p}_{ij}+\frac{m}{2}-1)$

Obtain the ordering vector of matrix PWhereinRepresent the relative order of i-th aircraft Vector magnitude；

(3.5) utilizeI ∈ m is to colony synthesized attribute evaluation and test r_iIt is ranked up, and then aircraft lands risk is ranked up And preferentially, finally realize the evaluation and test of landing risk.